{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:URQYCAYDDBFVMJXVQFLJ35LEI4","short_pith_number":"pith:URQYCAYD","schema_version":"1.0","canonical_sha256":"a461810303184b5626f581569df5644700e6211f7e86fe00b1b7c2dea16fa2e3","source":{"kind":"arxiv","id":"q-alg/9709040","version":1},"attestation_state":"computed","paper":{"title":"Deformation quantization of Poisson manifolds, I","license":"","headline":"","cross_cats":["alg-geom","hep-th","math.AG","math.QA"],"primary_cat":"q-alg","authors_text":"Maxim Kontsevich","submitted_at":"1997-09-29T10:27:51Z","abstract_excerpt":"I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the set of equivalence classes of Poisson structures on X modulo diffeomorphisms. In fact, a more general statement is proven (\"Formality conjecture\"), relating the Lie superalgebra of polyvector fields on X and the Hochschild complex of the algebra of functions on X. Coefficients in explicit formulas for the deformed product can be interp"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"q-alg/9709040","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-09-29T10:27:51Z","cross_cats_sorted":["alg-geom","hep-th","math.AG","math.QA"],"title_canon_sha256":"13e2f17fcd043880f105b32b35bd1cba58e7d16f9a2eb29a8bceb86bb70a82dc","abstract_canon_sha256":"3f6d54c130dc2399066db6c4fae79d215770827f4ccaf863c28f86743350678e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:04.021760Z","signature_b64":"3YVK1uSL15sUF05T6T0ZvGnfnVRYZNNH3UHn52DZtNBuvFPgETcwrc4DsA/bFH8vfLC8tX6uJl0QnSirfZr4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a461810303184b5626f581569df5644700e6211f7e86fe00b1b7c2dea16fa2e3","last_reissued_at":"2026-05-18T04:20:04.021328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:04.021328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformation quantization of Poisson manifolds, I","license":"","headline":"","cross_cats":["alg-geom","hep-th","math.AG","math.QA"],"primary_cat":"q-alg","authors_text":"Maxim Kontsevich","submitted_at":"1997-09-29T10:27:51Z","abstract_excerpt":"I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the set of equivalence classes of Poisson structures on X modulo diffeomorphisms. In fact, a more general statement is proven (\"Formality conjecture\"), relating the Lie superalgebra of polyvector fields on X and the Hochschild complex of the algebra of functions on X. Coefficients in explicit formulas for the deformed product can be interp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9709040","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9709040","created_at":"2026-05-18T04:20:04.021389+00:00"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9709040v1","created_at":"2026-05-18T04:20:04.021389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9709040","created_at":"2026-05-18T04:20:04.021389+00:00"},{"alias_kind":"pith_short_12","alias_value":"URQYCAYDDBFV","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"URQYCAYDDBFVMJXV","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"URQYCAYD","created_at":"2026-05-18T12:25:48.327863+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2607.07785","citing_title":"Quantization of Gravity on Null Hypersurfaces","ref_index":99,"is_internal_anchor":true},{"citing_arxiv_id":"1907.00912","citing_title":"Problem of Time and Background Independence: classical version's higher Lie Theory","ref_index":41,"is_internal_anchor":true},{"citing_arxiv_id":"2605.22910","citing_title":"Flows on Graded Manifolds","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2602.15120","citing_title":"How to have your wormholes and factorize, too","ref_index":65,"is_internal_anchor":true},{"citing_arxiv_id":"2605.12173","citing_title":"Chaos and epoch structure in the deformed Mixmaster universe","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2604.23496","citing_title":"Q-Manifolds and Sigma Models","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.13163","citing_title":"Covariant phase space approach to noncommutativity in tensile and tensionless open strings","ref_index":80,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4","json":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4.json","graph_json":"https://pith.science/api/pith-number/URQYCAYDDBFVMJXVQFLJ35LEI4/graph.json","events_json":"https://pith.science/api/pith-number/URQYCAYDDBFVMJXVQFLJ35LEI4/events.json","paper":"https://pith.science/paper/URQYCAYD"},"agent_actions":{"view_html":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4","download_json":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4.json","view_paper":"https://pith.science/paper/URQYCAYD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=q-alg/9709040&json=true","fetch_graph":"https://pith.science/api/pith-number/URQYCAYDDBFVMJXVQFLJ35LEI4/graph.json","fetch_events":"https://pith.science/api/pith-number/URQYCAYDDBFVMJXVQFLJ35LEI4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4/action/storage_attestation","attest_author":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4/action/author_attestation","sign_citation":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4/action/citation_signature","submit_replication":"https://pith.science/pith/URQYCAYDDBFVMJXVQFLJ35LEI4/action/replication_record"}},"created_at":"2026-05-18T04:20:04.021389+00:00","updated_at":"2026-05-18T04:20:04.021389+00:00"}